基于扩散函数的内集-外集模型

内集-外集模型用于计算小样本事件的可能性-概率分布(PPD),以表达概率估计的模糊性。基于分配函数的内集-外集模型存在三点不足:①论域步长的选取随意性太大;②PPD值在0.5到1之间无值;③信息过于集中,PPD值在很多区间值为0。本文从解决此三问题入手,对传统模型进行了改进。首先讨论了论域步长选取的合理性问题;其次引入扩散函数替换分配函数,同时解决了问题②和③;最后,仿真实验的结果显示,改进模型的估计比传统模型的估计更接近于真实分布。     

一个物体运动的优化模型及应用

建立了一类具广泛应用价值的物体运动非线性泛函优化模型,包括目标泛函,决策函数,约束条件,可行函数空间.决策函数是能量消耗分配函数,可行函数空间中的能量消耗分配函数确定目标泛函值,该模型的最优解是使目标泛函值最大的能量分配函数.这个非线性泛函优化模型,表述了一类物体运动能量转化为机械功的实际问题.例如机动车行驶中如何控制燃料消耗方式,使燃油消耗最少.运动员在赛跑中如何分配体能消耗使成绩最好等.该文从非线性泛函变分及优化理论角度对该模型进行了定量探讨.所得结果可应用于物体运动功能转化相关实际问题中.该文也提出了若干公开问题.     

分配格上函数差的共轭函数的一般公式

对于分配酪上的任意函数f:D→R和子模函数g:D→R,利用f和g的共轭函数,我们给出了(f-g)的共轭函数的一个公式,作为它的应用,我们得到了Fujishije的对偶定理。     

风险分配与风险预算管理

本文首先引入风险度量定义,分析了无组合效应风险与可互换风险这两种具有特殊性质的个体风险特征,在此基础上我们讨论了风险分配应该满足的原则.我们证明并比较了在标准差风险度量下,协方差风险分配函数与相对风险分配函数性质上的差异,并证明风险预算也是一种特殊形式的风险分配函数.最后我们给出不同风险分配函数之间的联系.     

齐次生产函数条件下长期成本函数的确定方法

文章研究一般性齐次生产函数条件下长期成本函数的确定方法，证明了长期成本函数是关于产量的幂函数，并指出了长期边际成本函数和长期平均成本函数之间的特殊关系。     

具有区间支付的合作对策的区间Shapley值

针对合作对策中支付函数是区间数的情形,利用区间数运算的性质,对Shapley值在经典意义下的三条公理进行拓广,并论证了该形式下的Shapley 函数的唯一形式,并将区间Shapley值方法应用到供应链协调利益分配的实例中.由于支付函数是区间数,本文最终给出的分配的结果也是一个区间数.通过证明可知,由各个联盟对应区间支付范围内的不同实数值所组成的对策是经典合作对策,并且其Shapley值一定包含在区间Shapley值中.     

博弈联盟模糊收益的分配

提出了联盟模糊收益合理分配的一种新方法.首先,在模糊收益α截集上定义了α合理分配集,分析了该分配集与模糊收益Shapley值的关系.接着,给出了模糊收益的α合理Shapley分配函数,对其性质进行了讨论.然后,构造了模糊合理Shapley分配,证明其连续性,得到了联盟模糊收益与模糊合理Shapley分配具有包含关系的结论.     

可加号的门诊预约能力分配问题

预约服务可以有效优化医院门诊就诊流程,针对我国患者预约意识不强和预约患者爽约率高的特点,本文研究患者需求量较高时可以增加号源的条件下,考虑加号和拒绝患者成本,以门诊收益期望最大为目标,匹配预约患者和现场挂号患者需求量的能力分配问题。证明了门诊收益期望函数的单峰性,给出了最优解满足的条件。通过大量数值实验分析不同参数对门诊能力分配方案的影响,结果表明两类患者需求量对能力分配方案有较大影响,可加号情况下能力分配方案对患者爽约更敏感。     

基于点X=0的均值函数的性质及其应用

研究平均值函数φ（x）=1/x∫0^xf（t）dt,利用微积分学的有关概念,得到了它和被积函数具有相同或相似的奇偶性、周期性、单调性、连续性、可导性等性质,并配有应用实例．     

中国三次产业结构与初次分配结构变动关系的实证研究

构造了考虑产业结构影响的柯布-道格拉斯生产函数模型,利用我国1990-2009年的跨产业部门时间系列数据,采用岭回归的方法计算出三次产业比重对要素产出弹性的影响系数,以2009年的数据为基础,分析了产业结构变动对初次分配结构的影响,研究结果表明,工业化是劳动报酬份额下降的原因,而加强农业的基础地位、稳步推进以第三产业为主导的经济转型有助于改善初次分配恶化的局面。     

A cost allocation problem arising in hub–spoke network systems

This paper studies a cost allocation problem arising from hub–spoke network systems. When a large-scale network is to be constructed jointly by several agents, both the optimal network design and the fair allocation of its cost are essential issues. We formulate this problem as a cooperative game and analyze the core allocation, which is a widely used solution concept. The core of this game is not necessarily non-empty as shown by an example. A reasonable scheme is to allocate the cost proportional to the flow that an agent generates. We show that, if the demand across the system has a block structure and the fixed cost is high, this cost allocation scheme belongs to the core. Numerical experiments are given with real telecommunication traffic data in order to illustrate the usefulness of our analytical findings.     

Resource Allocation with Wobbly Functions

We consider resource allocation with separable objective functions defined over subranges of the integers. While it is well known that (the maximisation version of) this problem can be solved efficiently if the objective functions are concave, the general problem of resource allocation with functions that are not necessarily concave is difficult.In this article, we focus on a large class of problem instances, with objective functions that are close to a concave function or some other smooth function, but with small irregularities in their shape. It is described that these properties are important in many practical situations.The irregularities make it hard or impossible to use known, efficient resource allocation techniques. We show that, for this class of functions the optimal solution can be computed efficiently. We support our claims by experimental evidence. Our experiments show that our algorithm in hard and practically relevant cases runs up to 40–60 times faster than the standard method.     

Allocation of jobs and identical resources with two pooling centers

We examine the resource allocation problem of partitioning identical servers into two parallel pooling centers, and simultaneously assigning job types to pooling centers. Each job type has a distinct Poisson arrival rate and a distinct holding cost per unit time. Each pooling center becomes a queueing system with an exponential service time distribution. The goal is to minimize the total holding cost. The problem is shown to be polynomial if a job type can be divided between the pooling centers, and NP-hard if dividing job types is not possible. When there are two servers and jobs cannot be divided, we demonstrate that the two pooling center configuration is rarely optimal. A heuristic which checks the single pooling center has an upper bound on the relative error of 4/3. The heuristic is extended for the multiple server problem, where relative error is bounded above by the number of servers.      

Cost allocation and convex data envelopment

This paper considers allocation rules. First, we demonstrate that costs allocated by the Aumann–Shapley and the Friedman–Moulin cost allocation rules are easy to determine in practice using convex envelopment of registered cost data and parametric programming. Second, from the linear programming problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output) variables and hence enable a full allocation of the inefficiency on to the input (or output) variables as in the CCR model.     

具有内生基础设施分配的城市经济增长模型

In this paper, an urban economic growth model with endogenous infrastructure allocation is given by introducing the two-variable utility function for city＇s inhabitant. A twodimensional dynamical system is obtained by solving the utility maximization problem and it is proved that this system has the unique non-zero equilibrium which is a saddle. The model has the unique optimal growth and an optimal rate of infrastructure allocation.     

A polynomial expression for the Owen value in the maintenance cost game

The class of maintenance cost games was introduced in 2000 to deal with a cost allocation problem arising in the reorganization of the railway system in Europe. The main application of maintenance cost games regards the allocation of the maintenance costs of a facility among the agents using it. To that aim it was first proposed to utilize the Shapley value, whose computation for maintenance cost games can be made in polynomial time. In this paper, we propose to model this cost allocation problem as a maintenance cost game with a priori unions and to use the Owen value as a cost allocation rule. Although the computation of the Owen value has exponential complexity in general, we provide an expression for the Owen value of a maintenance cost game with cubic polynomial complexity. We finish the paper with an illustrative example using data taken from the literature of railways management.     

排序对策的一个新的收益分配准则

针对一个机器的排序问题,给出了排序问题中成本增加量的表达式,提出了收益分配的不小于成本增加量准则。针对一类特殊的排序问题,给出一个符合不小于成本增加量分配准则的解,并证明了它满足有效性,哑元性和单调性。结合一个算例,对本文的提出的方法进行了分析验证。     

Fixed cost and resource allocation based on DEA cross-efficiency

In many managerial applications, situations frequently occur when a fixed cost is used in constructing the common platform of an organization, and needs to be shared by all related entities, or decision making units (DMUs). It is of vital importance to allocate such a cost across DMUs where there is competition for resources. Data envelopment analysis (DEA) has been successfully used in cost and resource allocation problems. Whether it is a cost or resource allocation issue, one needs to consider both the competitive and cooperative situation existing among DMUs in addition to maintaining or improving efficiency. The current paper uses the cross-efficiency concept in DEA to approach cost and resource allocation problems. Because DEA cross-efficiency uses the concept of peer appraisal, it is a very reasonable and appropriate mechanism for allocating a shared resource/cost. It is shown that our proposed iterative approach is always feasible, and ensures that all DMUs become efficient after the fixed cost is allocated as an additional input measure. The cross-efficiency DEA-based iterative method is further extended into a resource-allocation setting to achieve maximization in the aggregated output change by distributing available resources. Such allocations for fixed costs and resources are more acceptable to the players involved, because the allocation results are jointly determined by all DMUs rather than a specific one. The proposed approaches are demonstrated using an existing data set that has been applied in similar studies.     

Single-machine scheduling with time-and-resource-dependent processing times

We consider single-machine scheduling problems in which the processing time of a job is a function of its starting time and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. We show that the problems remain polynomially solvable under the proposed model.